Everytime I have read about this (web posts or magazines), they always say NOT to put running shoes in the washing machine.
For one it is not good for the materials and glues of a quality running shoe.
Just shake em out, the best you can and use a wet washcloth to give em a once over. One of the best inventions ever made by mankind is a can of compressed air (the kind you use to clean your computer monitor and keyboard). Use that to blow off as much dirt as you can from the inside.
I always keep finding great ideas for compressed air.

If they are looking dirty because you have worn them everyday for over a year, than it may be time for a new pair.
I wonder....
If you can get around 500 miles out of a pair of shoes, I bet that the ppl who run 100 mile weeks must have some really brand new looking shoes when they get rid of them.
Any 100mpw ppl disagree???